A uniform distribution is where the probability of every outcome is the same.
For discrete data, this is a probability of 1/N for each value, where N is the number of values. In the case of data 1...N the mean (μ) is (N+1)/2 and the variance is (N+1)(N-1)/12
For bounded continuous data the probability is 1/W where W is the width of the data.. In the case of continuous data over [0,W] the mean (μ) is W/2 and the variance is W^{2}/12

Note that in the continuous case, the definitin of 'uniform' depends on the form of the parameter. For example, if dealing with sound waves a uniform distrubution over the wavelength is a different probability distribution to one that is uniform over the frequency.